Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A111125 → basis A007318
  1 · 4, 1 · 11, 7, 1 · 29, 31, 10, 1 … Σ 1, 5, 19, 71, 265, 989, 3691, 13775, …
  (−5, −1)nonnegative
• A152842 → x ↦ x+1
  1 · 4, 3 · 8, 10, 3 · 32, 64, 42, 9 … Σ 1, 7, 21, 147, 441, 3087, 9261, 64827, …
  (−∞, −1]nonnegativerational roots
• A038255 → basis A013610
  1 · 7, 3 · 49, 42, 9 · 343, 441, 189, 27 … Σ 1, 10, 100, 1000, 10000, 100000, …
  (−∞, −1]nonnegativerational roots
• A100862 → θ+1
  1 · 1, 2 · 1, 6, 3 · 1, 12, 18, 4 … Σ 1, 3, 10, 35, 129, 497, 1996, 8325, …
  (−∞, 0]nonnegative
• A038338 → basis A013610
  576, 1728, 1296 · 13824, 62208, 93312, 46656 … Σ 3600, 216000, 12960000, 777600000, …
  [−1, 0]nonnegativerational roots
• basis-map coefficients of A030528, shifted → reverse
  1 · -1 · 1 · -1 … Σ 1, -1, 1, -1, 1, -1, 1, -1, …
  (−∞, 0]rational roots
• A038259 → θ+1
  1 · 6, 10 · 36, 120, 75 · 216, 1080, 1350, 500 … Σ 1, 16, 231, 3146, 41261, 527076, …
  (−∞, 0]nonnegativerational roots
• A358735 → θ+1
  1 · 1, 2 · 1, 8, 6 · 1, 20, 48, 24 … Σ 1, 3, 15, 93, 675, 5587, 51845, 532705, …
  (−∞, 0]nonnegative
• A054142 → D → θ+1
  1 · 3, 4 · 5, 24, 9 · 7, 60, 90, 16 … Σ 0, 1, 7, 38, 173, 701, 2628, 9329, …
  (−∞, 0]nonnegative
• A130123 → (θ+1)² → reverse
  1 · 8 · 36 · 128 … Σ 1, 8, 36, 128, 400, 1152, 3136, 8192, …
  (−∞, 0]nonnegativerational roots
• delannoy → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 20, 45, 16 … Σ 1, 5, 22, 82, 283, 923, 2892, 8788, …
  (−∞, 0]nonnegative
• A269947 → reverse
  1 · 1 · 1, 1 · 1, 9, 8 … Σ 1, 1, 2, 18, 504, 32760, 4127760, …
  (−∞, 0]nonnegativerational roots
• A013612 → x ↦ x+1 → D+1
  96, 110, 25 · 756, 1440, 825, 125 … Σ 231, 3146, 41261, 527076, 6603091, …
  (−∞, 0]nonnegativerational roots
• A049403 → reverse
  1, 3 · 1, 6, 3 · 1, 10, 15 · 1, 15, 45, 15 … Σ 4, 10, 26, 76, 232, 764, 2620, 9496, …
  (−∞, 0]nonnegative
• A137338 → D
  1 · -3, 2 · 6, -12, 3 · -9, 52, -30, 4 … Σ 0, 1, -1, -3, 17, -57, 179, -631, …
  (−∞, ∞)
• A106800 → x ↦ x+1 → x ↦ x+1
  1 · 1 · 3, 1 · 11, 7, 1 … Σ 1, 1, 4, 19, 109, 742, 5815, 51193, …
  (−∞, −1]nonnegative
• A143685 → basis A007318 → x ↦ x/(x+1)
  1 · 2, 3 · 13, 39, 27 · 44, 198, 288, 135 … Σ 1, 5, 79, 665, 7591, 73865, 779239, …
  [−1, 0]nonnegative
• A038277 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 18, 29 · 324, 1044, 841 … Σ 1, 47, 2209, 103823, 4879681, …
  [−1, 0]nonnegativerational roots
• A134082 → (θ+1)²
  1 · 2, 4 · 0, 16, 9 · 0, 0, 54, 16 … Σ 1, 6, 25, 70, 153, 286, 481, 750, …
  (−∞, 0]nonnegativerational roots
• A104978 → (θ+1)²
  1 · 1, 4 · 2, 20, 27 · 5, 84, 252, 192 … Σ 1, 5, 49, 533, 5985, 68005, 776225, …
  (−∞, 0]nonnegative
• A008288 → basis A013610 → D+1
  1 · 5, 3 · 20, 33, 9 · 66, 198, 153, 27 … Σ 1, 8, 62, 444, 3050, 20344, 132838, …
  (−∞, 0]nonnegative
• A207606 → x ↦ x+1 → x ↦ x+1
  26, 15, 2 · 97, 84, 23, 2 · 362, 418, 174, 31, 2 … Σ 43, 206, 987, 4729, 22658, 108561, …
  (−6, −2)nonnegative
• A071951 → θ+1
  1 · 2, 2 · 4, 16, 3 · 8, 104, 60, 4 … Σ 1, 4, 23, 176, 1697, 20100, 286127, …
  (−∞, 0]nonnegative
• A152198 → D
  1 · 1 · 2, 2 · 2, 2 … Σ 0, 0, 1, 1, 4, 4, 12, 12, …
  (−∞, 0]nonnegativerational roots
• A038279 → basis A013611 → D+1
  1 · 13, 4 · 153, 104, 16 · 1701, 1836, 624, 64 … Σ 1, 17, 273, 4225, 63713, 942513, …
  (−∞, 0]nonnegativerational roots
• A038255 → basis A013609 → D
  2 · 28, 8 · 294, 168, 24 · 2744, 2352, 672, 64 … Σ 0, 2, 36, 486, 5832, 65610, 708588, …
  (−∞, 0]nonnegativerational roots
• A063967 → basis A013609 → reverse
  1 · 2, 2 · 4, 10, 6 · 8, 32, 40, 16 … Σ 1, 4, 20, 96, 464, 2240, 10816, 52224, …
  (−∞, 0]nonnegative
• A133080 → (θ+1)²
  1 · 1, 4 · 0, 0, 9 · 0, 0, 9, 16 … Σ 1, 5, 9, 25, 25, 61, 49, 113, …
  (−∞, 0]nonnegativerational roots
• A038279 → basis A013610 → reverse
  1 · 3, 9 · 9, 54, 81 · 27, 243, 729, 729 … Σ 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0]nonnegativerational roots
• A100861 → θ+1
  1 · 1 · 1, 2 · 1, 6 … Σ 1, 1, 3, 7, 22, 66, 226, 778, …
  (−∞, 0]nonnegative
• A091044 → basis A007318 → D
  2 · 16, 6 · 96, 80, 12 · 512, 672, 240, 20 … Σ 0, 2, 22, 188, 1444, 10446, 72714, …
  (−∞, −1]nonnegative
• A286718 → basis A013610 → x ↦ x/(x+1)
  1 · 2, 5 · 10, 41, 40 · 80, 438, 771, 440 … Σ 1, 7, 91, 1729, 43225, 1339975, …
  [−1, 0]nonnegativerational roots
• A357613 → x ↦ x/(x+1)
  1 · 3, 5 · 15, 50, 41 · 84, 420, 693, 377 … Σ 1, 8, 106, 1574, 24598, 395768, …
  [−1, 0]nonnegative
• A172431 → θ+1
  1 · 1, 4 · 1, 8, 9 · 1, 12, 30, 16 … Σ 1, 5, 18, 59, 185, 564, 1685, 4957, …
  (−∞, 0]nonnegative
• A103633 → basis A013609 → D
  2 · 6, 8 · 10, 32, 24 · 24, 104, 144, 64 … Σ 0, 2, 14, 66, 336, 1296, 6048, 21600, …
  (−∞, 0]nonnegativerational roots
• A110552 → D+1
  1 · 3, 2 · 6, 13, 4 · 11, 44, 41, 8 … Σ 1, 5, 23, 104, 468, 2096, 9328, 41216, …
  (−∞, 0]nonnegative
• narayana → basis A007318 → (θ+1)²
  1 · 2, 4 · 5, 20, 9 · 14, 84, 81, 16 … Σ 1, 6, 34, 195, 1131, 6608, 38788, …
  (−∞, 0]nonnegative
• A008955 → basis A013609 → D+1
  1 · 4, 2 · 36, 58, 16 · 540, 1696, 1492, 288 … Σ 1, 6, 110, 4016, 243376, 22063776, …
  (−∞, 0]nonnegative
• A038226 → basis A013609 → reverse
  256, 352, 121 · 4096, 8448, 5808, 1331 … Σ 729, 19683, 531441, 14348907, …
  (−∞, 0]nonnegativerational roots
• A013610 → basis A007318 → (θ+1)²
  1 · 4, 12 · 16, 96, 81 · 64, 576, 972, 432 … Σ 1, 16, 193, 2044, 20041, 186592, …
  (−∞, 0]nonnegative
• A063007 → D
  2 · 6, 12 · 12, 60, 60 · 20, 180, 420, 280 … Σ 0, 2, 18, 132, 900, 5910, 37926, …
  (−∞, 0]nonnegative
• A038334 → D+1
  336, 320, 64 · 5184, 8064, 3840, 512 … Σ 720, 17600, 416000, 9600000, 217600000, …
  (−∞, 0]nonnegativerational roots
• A104684 → basis A013610 → reverse
  1 · 3, 3 · 9, 24, 13 · 27, 135, 171, 63 … Σ 1, 6, 46, 396, 3606, 33876, 324556, …
  (−∞, 0]nonnegative
• A173018 → reverse (shift +1) → (θ+1)²
  1 · 0, 4 · 0, 4, 9 · 0, 4, 36, 16 … Σ 1, 4, 13, 56, 304, 1980, 15000, 129360, …
  (−∞, 0]nonnegative
• A145324 → D+1
  1 · 3, 2 · 6, 17, 6 · 10, 61, 98, 24 … Σ 1, 5, 29, 193, 1458, 12366, 116568, …
  (−∞, 0]nonnegative
• A143491 → basis A013610 → D+1
  33, 39, 9 · 201, 357, 189, 27 … Σ 81, 774, 7974, 88812, 1067652, …
  (−∞, 0]nonnegative
• A088996 → D
  1 · 1, 4 · 2, 14, 18 · 6, 58, 138, 96 … Σ 0, 1, 5, 34, 298, 3207, 40947, 605076, …
  (−∞, 0]nonnegative
• A178821 → Veronese 2 (j=1) → (θ+1)²
  5 · 30 · 105, 140 · 280, 1120 … Σ 0, 5, 30, 245, 1400, 6804, 29400, …
  (−∞, 0]nonnegative
• A091044 → basis A013609 → θ+1
  1 · 4, 8 · 16, 64, 36 · 64, 384, 480, 128 … Σ 1, 12, 116, 1056, 9296, 79936, 675392, …
  (−∞, 0]nonnegative
• A052553 → basis A008277 → θ+1
  1 · 1 · 2, 2 · 3, 4 … Σ 1, 1, 4, 7, 20, 43, 113, 267, …
  (−∞, 0]nonnegative